Hello good MHF folk. I'm getting very frustrated with a few exercises in Stroud's Advanced Engineering Mathematics 5th ed. I just can't get to the answers provided, I'm hoping someone may be able to help me

First one is this. Sketch the graph then find the laplace transform of:

I can draw the graph ok, I understand that. And my answer is almost the same but there is an

in the given answer that I just don't understand... Here is their answer: